GATE_PROJ
Top 16 Positive Activations
Rollout 0, Act: 0.012
<|im_start|>system\nYou are a helpful mathematics assistant.\n<|im_start|>user
Rollout 1, Act: 0.012
<|im_start|>system\nYou are a helpful mathematics assistant.\n<|im_start|>user
Rollout 2, Act: 0.012
<|im_start|>system\nYou are a helpful mathematics assistant.\n<|im_start|>user
Rollout 3, Act: 0.012
<|im_start|>system\nYou are a helpful mathematics assistant.\n<|im_start|>user
Rollout 4, Act: 0.012
<|im_start|>system\nYou are a helpful mathematics assistant.\n<|im_start|>user
Rollout 11, Act: 0.012
<|im_start|>system\nYou are a helpful mathematics assistant.\n<|im_start|>user
Rollout 6, Act: 0.012
<|im_start|>system\nYou are a helpful mathematics assistant.\n<|im_start|>user
Rollout 7, Act: 0.012
<|im_start|>system\nYou are a helpful mathematics assistant.\n<|im_start|>user
Rollout 8, Act: 0.012
<|im_start|>system\nYou are a helpful mathematics assistant.\n<|im_start|>user
Rollout 9, Act: 0.012
<|im_start|>system\nYou are a helpful mathematics assistant.\n<|im_start|>user
Rollout 10, Act: 0.012
<|im_start|>system\nYou are a helpful mathematics assistant.\n<|im_start|>user
Rollout 16, Act: 0.012
<|im_start|>system\nYou are a helpful mathematics assistant.\n<|im_start|>user
Rollout 12, Act: 0.012
<|im_start|>system\nYou are a helpful mathematics assistant.\n<|im_start|>user
Rollout 13, Act: 0.012
<|im_start|>system\nYou are a helpful mathematics assistant.\n<|im_start|>user
Rollout 14, Act: 0.012
<|im_start|>system\nYou are a helpful mathematics assistant.\n<|im_start|>user
Rollout 15, Act: 0.012
<|im_start|>system\nYou are a helpful mathematics assistant.\n<|im_start|>user
Top 16 Negative Activations
Rollout 21, Act: -6.294
→Z with such regularity (like satisfying additivity and certain functional equations) might have to be constant
Rollout 49, Act: -6.295
has countable spread and is T5 (hereditary normal), which we might or might not have,
Rollout 46, Act: -6.298
with angular velocity ��. The acceleration in the inertial frame is a_inertial = a_rot
Rollout 21, Act: -6.300
the image is the entire set Z. So surjective onto Z. So functions in X are surjective
Rollout 46, Act: -6.307
, which are usually part of the potential in an inertial frame. The last term is similar to a
Rollout 81, Act: -6.333
confusing; angle BAC is just one angle at vertex A, but perhaps in terms of coordinate geometry,
Rollout 21, Act: -6.335
1}, which are subsets of Z, not surjective onto Z. So S would not be a subset
Rollout 21, Act: -6.336
holds for the identity function is trivial. For surjective functions, injective functions, since 2f
Rollout 72, Act: -6.338
:\n\nIn a regular pentagon, the diagonal over side is the golden ratio φ = (1 + sqrt
Rollout 1, Act: -6.345
Compare to the above line:\n\nFrom the sum of norms, we have:\n\n-⟨x + x',
Rollout 21, Act: -6.372
. But to have image exactly Z, the surjective. If a function f satisfies f(x -f
Rollout 46, Act: -6.417
to the gradient of U? But only in an inertial frame would the acceleration equal the gradient of the
Rollout 46, Act: -6.431
? However, that would be the case in an inertial frame, but the presence of the centrifugal
Rollout 46, Act: -6.432
\n\nBut these would correspond to the acceleration in an inertial frame minus the centrifugal acceleration? I'm
Rollout 46, Act: -6.495
, without considering the rotating frame, so assuming an inertial frame where U is the conventional gravitational potential,
Rollout 84, Act: -6.614
and "twice as much" are both adverbial phrases modifying the verbs "purchased" and
UP_PROJ
Top 16 Positive Activations
Rollout 7, Act: 3.364
$47$ .\n<|im_start|>assistant\n<|im_start|>think\nAlright, so I'm trying to solve this
Rollout 44, Act: 3.314
mathrm{T}_{2}$\n<|im_start|>assistant\n<|im_start|>think\nOkay, so I need to figure out which
Rollout 26, Act: 3.305
mol}^{-1}$ ]\n<|im_start|>assistant\n<|im_start|>think\nOkay, let's try to figure this problem
Rollout 98, Act: 3.256
\n(D) 2\n<|im_start|>assistant\n<|im_start|>think\nOkay, so I need to figure out how
Rollout 6, Act: 3.238
$ . [/*]\n<|im_start|>assistant\n<|im_start|>think\nOkay, let me try to work through these
Rollout 94, Act: 3.231
\n(D) a,b\n<|im_start|>assistant\n<|im_start|>think\nOkay, so I need to determine which of
Rollout 18, Act: 3.215
=H_{xy}$ .\n<|im_start|>assistant\n<|im_start|>think\nAlright, let's tackle this problem step by
Rollout 45, Act: 3.193
of $ m$ .\n<|im_start|>assistant\n<|im_start|>think\nAlright, so I have this problem where a
Rollout 36, Act: 3.189
. Find $AP.$\n<|im_start|>assistant\n<|im_start|>think\nOkay, let me try to figure out how
Rollout 29, Act: 3.182
\rho gH$ \n<|im_start|>assistant\n<|im_start|>think\nOkay, let me try to figure out this
Rollout 23, Act: 3.180
555 Bq\n<|im_start|>assistant\n<|im_start|>think\nOkay, let's tackle this problem step by
Rollout 79, Act: 3.179
facility (8,4)\n<|im_start|>assistant\n<|im_start|>think\nOkay, let's tackle this crossword clue.
Rollout 54, Act: 3.174
, B = 2\n<|im_start|>assistant\n<|im_start|>think\nOkay, let's tackle this question step by
Rollout 1, Act: 3.172
mathcal{H}$ .\n<|im_start|>assistant\n<|im_start|>think\nOkay, so I need to show that there
Rollout 11, Act: 3.169
.\n\n*David Altizio*\n<|im_start|>assistant\n<|im_start|>think\nOkay, so I have this problem here where
Rollout 55, Act: 3.157
018}.$\n<|im_start|>assistant\n<|im_start|>think\nAlright, so I have this matrix A and
Top 16 Negative Activations
Rollout 22, Act: -2.270
T/m)\n\nv_mean = sqrt(8kT/(πm))\n\nAlright, so first I need
Rollout 54, Act: -2.275
ide (strong base)\n\n5. Ethanethiolate (weaker base than hydroxide)\n\n3
Rollout 15, Act: -2.280
- The system can be represented by a tridiagonal matrix \( M \) where each row has
Rollout 54, Act: -2.291
is most hydrated)\n- RS− (thiolate) is a better nucleophile than RO− (
Rollout 54, Act: -2.291
, methanol (neutral), ethanethiolate. Propionate is a carboxylate,
Rollout 54, Act: -2.294
Ka around 10, ethanethiolate (R-S−) would have a base strength
Rollout 54, Act: -2.302
base (strongest acid), ethanethiolate next (still weaker base than hydroxide and
Rollout 26, Act: -2.307
Delta H_f^\circ (\mathrm{HgO}) = \frac{-180.7
Rollout 97, Act: -2.315
may not be precise. Because the reaction stoichiometry is moles, but in terms of partial pressures
Rollout 54, Act: -2.340
bases.\n\nThus, even though ethanethiolate (5) is a weaker base than hydrox
Rollout 54, Act: -2.345
) > hydroxide > ethanethiolate > propionate (weakest base).\n\nThen,
Rollout 54, Act: -2.345
:\n\nOrder: 5 (ethanethiolate) > 2 (hydroxide) >
Rollout 54, Act: -2.410
solution:\n\nIn SN2 reactions, the thiolate ion (e.g., SH−) is a
Rollout 22, Act: -2.426
are:\n\nv_rms = sqrt(3kT/m)\n\nv_mean = sqrt(8kT
Rollout 15, Act: -2.537
Such matrices are called Jacobi matrices or tridiagonal matrices. Nilpotency can be discussed via their
Rollout 15, Act: -2.596
polynomial is x^n.\n\nBut for any tridiagonal matrix, particularly symmetric ones, eigenvalues are real
DOWN_PROJ
Top 16 Positive Activations
Rollout 79, Act: 2.599
use: M, I, N, O, R, C, H, A, N, G
Rollout 79, Act: 2.588
– letters M, I, N, O, R, C, H, A, N, G
Rollout 79, Act: 2.533
changes": M, I, N, O, R, C, H, A, N, G
Rollout 79, Act: 2.529
changes": M, I, N, O, R, C, H, A, N, G
Rollout 79, Act: 2.476
again: M, I, N, O, R, C, H, A, N, G
Rollout 79, Act: 2.465
" : M, I, N, O, R, C, H, A, N, G
Rollout 79, Act: 2.461
changes": M, I, N, O, R, C, H, A, N, G
Rollout 79, Act: 2.446
letters (M, I, N, O, R, C, H, A, N, G
Rollout 79, Act: 2.435
letters: M, I, N, O, R, C, H, A, N, G
Rollout 79, Act: 2.414
letters (M, I, N, O, R, C, H, A, N, G
Rollout 79, Act: 2.409
letters: M, I, N, O, R, H, N, G. Let's see
Rollout 79, Act: 2.395
check: M, I, N, O, R plus H, G, N. That could be
Rollout 79, Act: 2.385
has letters M, I, N, O, R, C, H, A, N, G
Rollout 79, Act: 2.375
letters: M, I, N, O, R, C, H, A, N, G
Rollout 79, Act: 2.373
have are M, I, N, O, R, C, H, A, N, G
Rollout 79, Act: 2.336
) are M, I, N, O, R, C, H, A, N, G
Top 16 Negative Activations
Rollout 79, Act: -1.375
".\n\nSo maybe "minor changes" is an anagram for the answer. Let's try to rearrange
Rollout 49, Act: -1.380
union of closed sets) is called a "perfectly normal" space? Not exactly. Perfectly normal
Rollout 79, Act: -1.382
answer is "something something" that's an anagram of "minor changes" plus some letters. Wait
Rollout 79, Act: -1.382
. So maybe "minor changes" is the anagram fodder, which would form an 8-letter word
Rollout 79, Act: -1.388
". The wordplay usually involves some kind of anagram, reversal, hidden word, etc. "Not
Rollout 39, Act: -1.390
9... part becomes 111... and then 7101 becomes 789
Rollout 79, Act: -1.397
again.\n\nIf "Noticed" is the anagram indicator, then anagram of "minor changes in
Rollout 79, Act: -1.403
's see. If "noticed" is the anagram indicator, then "minor changes" has to be
Rollout 51, Act: -1.424
variable to y = x - ��, and then considering the integral from -θ to 2π
Rollout 79, Act: -1.427
, then "minor changes" has to be anagrammed. Let's check the letters. "Minor
Rollout 74, Act: -1.456
fore-and-aft component K_b (proportional to the Earth's field?) and athwartships
Rollout 57, Act: -1.462
pen sets. Wait, perhaps regularity is a result of the density topology being a regular topology through its
Rollout 79, Act: -1.483
etc. "Noticed" might be the anagram indicator. "Minor changes" could be the letters
Rollout 62, Act: -1.532
−m+11.](https://oeis.org/search?q=%22m%5E
Rollout 79, Act: -1.571
words from these letters include:\n\n- "Hernias" plus some others. No. Maybe "Chair
Rollout 23, Act: -1.590
You are a helpful mathematics assistant.\n<|im_start|>user\nImagine a radioactive nuclei X(Z,A) can decay into